Answer to Question #156769 in Mechanics | Relativity for joy

Question

1. Draw a graph to show that acceleration is proportional to inverse of mass?

2. Draw a graph that relates the mass and acceleration of a moving object?

3.What is the relationship between force, mass and acceleration?

4. What is deceleration?

5. What do you mean by one newton of force?

Answer 1

Explanations

• As it was discovered by Sir Isaac Newton, the net force, mass & acceleration are related to an object according to the relationship $\small F_{net}=ma$.
• For a constant net force, acceleration behaves in a manner proportional to the inverse of object's mass.

$\qquad\qquad \begin{aligned} \small a&= \small \frac{F_{net}}{m}\to a\propto\frac{1}{m} \end{aligned}$

• And it can be graph to as follows

• This means the same force generates lowered accelerations for bigger masses.

• If we think that the object continues to accelerate, this means it increases its speed. Any difference of its mass at normal speeds ( speeds lesser than the speed of light) is not detected but as it approaches the speed of light its mass can be thought to increase according to the following equations (very accurate forms of $\small F=ma$ and $\small E=mc^2$ ),

$\qquad\qquad \begin{aligned} \small F_{net}&= \small m\frac{du}{dt}\cdot\frac{1}{(1-\frac{u^2}{c^2})^{\frac{3}{2}}}\\ \end{aligned}$ and $\qquad\qquad \begin{aligned} \small E_{\text{total}}&= \small \frac{1}{\sqrt{1-\frac{u^2}{c^2}}} \cdot m c^2 \end{aligned}$

Where u is the instantaneous speed.

• Therefore, a graph like the following is obtained.

• Deceleration is the opposite of acceleration which could be thought of as a negative acceleration that decreases the speed. Rate of decrement of speed.

• One Newton is the force needed to accelerate an object having a mass of one kilogram by an acceleration of $\small 1ms^{-2}$